Mean Aversion in and Persistence of Shocks to the US Dollar: Evidence from Nine Foreign Currencies

Abstract

This paper analyses the statistical behavior of the US dollar, against nine different currencies, over the float period, with a monthly data set. The martingale hypothesis is rejected for all currencies. However, all currencies have a unit root. There is overwhelming evidence for significant positive serial correlation and ARCH effects in the logged series and in the changes of the logs. In addition, the nine logged series are characterized by structural breaks in both the intercept and the slope. Surprisingly, when the changes of the logs are considered, these do not show up any structural breaks, although the sample period has witnessed more than one political, social, and economic regime. All the nine logged currencies are well described by a low-order ARIMA model, with a parcimonious GARCH specification of the conditional variance. These ARIMA models imply mean aversion, rather than mean reversion, and high persistence of shocks. Mean aversion and persistence of shocks are formally tested and found to be significant for all nine currencies. This justifies the title of the paper.

Keywords

• US dollar, mean aversion, persistence of shocks, market efficiency, martingale, structural breaks, ARIMA, GARCH